1. Technical Field
This invention relates generally to radar systems, and particularly to those systems in which radar performance is not limited by internal noise, but rather by external sources such as electronic countermeasures (ECM) or by clutter arising from echoes from the land and/or sea. The proposed invention concerns the improvement in a radar system's ability to detect, distinguish and use target signals embedded in such ECM or clutter, by means of a correlation radar which employs a transmitter modulating function with a near optimum or optimal correlation function, which results in an optimal ambiguity function.
When operating in an ECM environment and/or in a background of land and/or sea clutter, performance improvements will be in obtained in both continuous wave (CW), and in pulse radar (PR) radar systems. Particular applicability will be found in: high, medium and low PRF pulse doppler (PD) radars used in search, acquisition and tracking radars; and in missile borne semi-active or active CW or pulse doppler radar homing seekers.
2. Background Art
The theory regarding the detectability of radar signals in noise has been well developed and is described at length in the open literature. Early references include:
1.) "Radar Systems Engineering", Ridenour, L. N. MIT Radiation Laboratory Series, McGraw-Hill Book Co., N.Y. , 1947 PA1 2.) "Radar Systems Analysis", Barton, D., Prentice-Hall Inc., Englewood Cliffs, N.J., 1964 PA1 3.) "Radar Handbook", Skolnick, M. I., McGraw-Hill Book Co., N.Y., 1970 PA1 4.) Berkowitz, R. S., "Modern Radar Analysis, Evaluation, and System Design", John Wiley & Sons, Inc., N.Y., 1965. PA1 a. the probability that a target has range delay t.sub.1 and doppler shift f.sub.1 is equal for all t and f.sub.d within a band of interest and is zero outside of that band. PA1 b. the output of the receiver be examined by a threshold device which determines the values of t and f.sub.d where the threshold has been exceeded. Condition a. requires that the target range and velocity, although not known are bounded. Condition b. specifies a simple and desirable (and conventional) receiver output processor.
The theory for the improvement of radar performance in a background of ECM or clutter is also well developed. This theory is concerned with target resolution, that is, separation of targets one from another and separation of targets embedded in a background of clutter or ECM. In radar signal analysis, this theory is described as `Ambiguity Theory` in, for example, references 3 and 4 above. Reviewing this material, one finds that much of the literature associated with optimum receivers is concerned with signal detection and target resolution in range and velocity. The following review of these concepts will aid in the understanding of this invention.
The initial consideration is that of signal detectability, or receiver sensitivity. If an optimum detection procedure is used, the sensitivity of a radar receiver depends only on the total energy of the received signal and not on its form. It is the energy density spectrum of the signal with respect to the energy density spectrum of the noise which determines the receiver's sensitivity.
Measures of resolution are not so easily perceived, except for simple waveforms. In a simple pulse radar, the resolving power of the transmitted pulse depends on the pulse duration. The narrower the pulse, the more closely two targets may approach each other in range before their echoes merge. From Fourier transform theory, we know that the narrower a pulse becomes, the broader its spectrum becomes. Thus range resolution is inherently inversely proportional to signal bandwidth. However, it has been shown in Reference 4 above, that it is the `effective` signal bandwidth that determines the range resolution properties of a signal. That is, signal duration is not directly involved in range resolution. Long duration and high bandwidth are not incompatible if a signal has rapid and/or irregular changes in its structure. In a like manner, the literature shows that velocity (doppler) resolution is inversely related to the signal `effective` duration.
FIG. 1 shows an example of delay and doppler ambiguity surfaces for monochromatic pulses. The central peak of the ambiguity function in the range direction will be narrow if the bandwidth is high, i.e. the greater the bandwidth the better the range resolution; and the central peak in the doppler direction will be narrow if the duration is long, i.e. the longer the duration the better the doppler resolution. A good rule is that the range resolution is approximately equal to 1/bandwidth and doppler resolution is approximately equal to 1/duration.
Radar ambiguity theory thus involves optimization of the Range-Velocity (t, f.sub.d) ambiguity function to yield optimal resolution of signals in the t, f.sub.d domain. The ideal ambiguity function is shown to resemble a thumbtack, that is it has a single spike at the origin (t.sub.0, f.sub.0) and is zero elsewhere. The receiver must process the signal in a manner such that both the range delay t and doppler frequency shift f.sub.d are determined. Due to noise t.sub.1 and f.sub.1 for any specific target can only be estimated. The literature shows that the very best that any receiver can do is to determine the probability that t.sub.1 =t.sub.0 and f.sub.1 =f.sub.0 for all measured paired values of t and f.sub.d. Once these probabilities are determined and presented at the receivers output, decisions can be made as to which specific paired values represent targets of interest. Thus, the ideal receiver must determine the joint probability density distribution of t and f.sub.d given the received signal e.sub.R (t). One desirable output for such a receiver is shown in FIG. 2. The shape of this probability density distribution is important because it describes the resolution capability of the system. The shape can be controlled by controlling the shape of the transmitted signal, that is, by controlling the modulation function.
Receivers that measure the joint probability density distribution are not realizable in a practical sense. Fortunately this joint probability density distribution has been shown in the literature to be linearly related to the envelope of the cross correlation function of the received and transmitted signals, provided that certain conditions are fulfilled. These conditions require:
Most radar receivers that operate in real time take advantage of this property of the cross correlation function and are designed to correlate the received signal with a delayed replica of the transmitted signal. This is particularly true for coherent systems such as doppler radars. The correlator is then followed by a threshold detector which determines the values of t and f.sub.d for which the threshold has been exceeded.
Thus the ideal realizable receiver for a radar system concerned with measurement of target range and doppler is a single channel, two-dimensional correlator that cross correlates the received signal with a delayed replica of the transmitted signal and maximizes the cross correlation function for the selected modulation function.
It was indicated above that the radar as a system must be optimized from the system viewpoint, i.e. the transmit and receive functions must be considered together. In the concepts reviewed above, it was shown that a receiver may be synthesized to provide optimum performance for any given modulation function. However, careful selection of the transmitter modulating function can maximize the peak of the joint ambiguity surface, and the goal is to strive to get as close as possible to the ideal ambiguity surface (a single, sharp central peak in the t, f.sub.d plane). This, we have shown, requires the effective signal bandwidth to be as large as possible to provide a sharp peak in the range dimension, and the signal duration must be long to provide a sharp peak in the frequency dimension (i.e., for good doppler resolution). Both of these conditions can be met using conventional spread spectrum waveforms. Selection of a special version of such a transmitted waveform has in turn led to the invention of a very simple processor providing the desired signal correlation which gives optimal range and doppler resolution.
Spread spectrum waveforms have been used for over 30 years in radar systems, and more recently in communication systems. The principle efforts in the radar field have been to extend the original linear-FM (chirp) waveforms developed at Bell Laboratories by using waveforms that have many of the desirable properties of the chirp waveforms. For example, the original chirp waveform was an intrapulse FM where the carrier frequency was swept linearly during the pulse `on-time`. More recent applications have used an inter-pulse FM sweep where longer modulation time periods and greater FM deviations are realized. These linear FM sweeps have been realized using either phase modulation or conventional FM techniques.
In an recent alternate approach, Walker, in U.S. Pat. No. 5,32,1409, describes a radar system utilizing chaotic coding, in which the code sequence is a series of numbers generated by a chaotic mapping difference equation. Such sequences are nonperiodic and unpredictable, while being readily correlatable. The random coding method of this invention however, uses random numbers, not those generated by a mapping procedure as for the chaotic codes.
Much of the literature is devoted to the analysis and application of pseudo-random sequences as modulating functions in spread spectrum radars and communication systems. Recent examples of these systems include U.S. Pat. No. 5,291,202 for Noise Radars to McClintock, in which a continuous transmitted signal is phase coded in pseudo-random sequences of long durations, such as 10,000 bits. The driving force behind such systems is perhaps the ease with which the pseudo-random sequences can be generated using digital processing techniques. Such a sequence can be generated using a shift register. Maximal length sequences are developed using various feedback connections. The maximal length sequences possess many of the properties of the linear-FM modulation functions and have good correlation functions, i.e., they can be made to significantly improve the ambiguity function from those systems not using pseudo-random sequences.
A problem with such pseudo-random sequences is remembering the very long sequences and providing appropriate delays to implement the required cross correlation of the target return signal with a delayed replica of the transmitted signal. The problem is obviously manageable, but requires computer memory and adequate speed to operate in real time. Another problem with pseudo-random sequences is that high sidelobes can appear sporadically in the recovered or correlated signal. The position of the sidelobes in the frequency spectrum is a function of the feedback connections on the shift register used to generate the pseudo-random sequence. Different feedback arrangements can be found to shift these sidelobes from one frequency position to another but the sidelobes are not eliminated. As will been seen below however, an optimal ambiguity function radar may be obtained by using a purely random sequence with uniformly distributed and very low level sidelobes in its correlation function, resulting in near optimum suppression of unwanted signals such as clutter.